A coded mimo-Ofdm system’s performance comparison of the spatial channel model and the onering channel model based on interpolatioxn techniques

ovember 28, 2019 Abstract In this paper, we consider to estimate the channel coefficient in the wideband and frequency selective multi- input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) system. The simulation is based on two channel models, one has been proposed by the 3rd Generation Partnership Project (3GPP) standard - the Spatial Channel Model (SCM) and the other is the Onering channel model, under the LTE Advanced standard for 4G in the suburban macro-cell environment. The obtained results show the symbol error rate (SER) value when using different interpolations (Linear, Sinc or Wiener) with the same input parameters. The Space Frequency Block Coding (SFBC) and minimum mean-squared error (MMSE) equalizer are also used for the simulation of the MIMO 2x2 systems. The SER results in the SCM channel model are lower than that obtained by the Onering channel model when employing the different interpolation methods. Keywords: MIMO-OFDM, Onering channel model, SCM channel model, SFBC, Wiener interpolation, Sinc interpolation, Linear interpolation 1. Introduction* Channel modelling method is used in the wideband channel model to design and optimize the communication systems. In the stochastic channel model, we use the measurement results to simulate to the statistical features from which are reproduced the channel's probability properties. The geometry‐based stochastic models (GBSM) and the parametric stochastic models (PSM) are in the group of stochastic channel model [1]. In the GBSM, the assumptions are given that the scatters are arranged in a geometrical form by using the physical principles of reflections, scattering, and diffractions of electromagnetic waves. The scatter’s statistical properties are described by the distribution of angle of arrival (AoA) and the angle of departure (AoD). The Onering channel model of GBSM has been shown for wideband and frequency selective channel model in the Fourth Generation Advanced Long Term Evolution (4G- LTE-A) in [2]. In the PSM, the transmission paths which divide into the sub‐paths of the paths, the AoA or AoD are narrated by the channel parameters in the * Corresponding author: Tel.: (+84) 989145909 Email: nga.nguyenthu1@hust.edu.vn measurement. Therefore, there is huge database for simulating those channel models. Based on the PSM channel model method, the Third Generation Partnership (3GPP) develops the spatial channel model (SCM) [3]. The SCM has been studied for non-line of sight (NLOS) model for suburban macro, urban macro and urban micro cell. Authors in [4] have compared the spatial correlation properties of both the SCM and the Onering channel model in suburban macro cell. Coding method SFBC which takes advantages of diversity in frequency selective channel transmission scheme and the equalizer MMSE [5] are combined to investigate the performance of the MIMO-OFDMA system in physic and medium access control (MAC) layer. By reducing the pilot overhead requirements, the interpolation algorithms are applied to the MIMO- OFDM receiver to estimate the coefficient of the channel. The interpolation techniques in [6]–[12] are based on the training sequence estimation or the pilot estimation. Journal of Science & Technology 139 (2019) 031-036 32 In this paper, we study the performance of the symbol error rate (SER) when using different interpolation methods (Linear, SI and Wiener) on those channel models in 2ì2 MIMO-OFDM system. The channel models are simulated by using the SCM channel model as well as the Onering channel model under the LTE-A standard in NLOS case. We also combine the SFBC and the MMSE detection to improve the effectiveness of the channel estimation. The structure of this paper is as follows: Section 2 studies the two channel modelling methods of the Onering and SCM channel by the cross-correlation functions. The interpolation techniques for 2ì2 MIMO-OFDM system are introduced in section 3 and 4. Section 5 shows the simulation results and discussions. Conclusions are given in Section 6. 2. The wideband and frequency selective Onering and SCM channel modelling methods Both of the channel models point out the closed form expression the channel impulse responses which depend on the same condition: the delay power function, the number of transmit and receive antennas. 2.1. The Onering channel modelling approach In [1-2], authors describer the Onering channel models as the scatters are arranged around the mobile station (MS), from which the scatters are assumed to locate on a ring with the radius 𝑅𝑅 as in Fig.1. x D R sd∆ ud∆ v MSα vα M S nΦB Sα BS nΦ B S m axΦ nS 𝜑𝜑ℒ −𝜑𝜑ℒ 𝜑𝜑ℒ−1 −𝜑𝜑ℒ−1 𝐼𝐼ℒ 𝐼𝐼ℒ 𝐼𝐼ℒ−1 𝐼𝐼ℒ−1 𝐼𝐼1 𝐼𝐼1 𝜑𝜑1 −𝜑𝜑1 𝑦𝑦 Fig. 1. The scatering Onering model [4] In the MIMO system with 𝑆𝑆 (𝑠𝑠 = 1,2, 𝑆𝑆) transmit antennas and 𝑈𝑈 (𝑢𝑢 = 1,2, 𝑈𝑈) receive antennas, 𝑑𝑑𝑠𝑠 and 𝑑𝑑𝑢𝑢 are the distance of base station (BS) and MS antenna element𝑠𝑠, respectively, the channel impulse response (CIR) in time domain modelled by the Onering channel method ℎ𝑢𝑢,𝑠𝑠𝑂𝑂𝑂𝑂(𝜏𝜏, 𝑡𝑡) is given as [1] with the angles αBS, αMS are the angles of the transmit antenna at the BS and of the receive antenna at the MS, respectively. ℎ𝑢𝑢,𝑠𝑠𝑂𝑂𝑂𝑂(𝜏𝜏, 𝑡𝑡)= � 𝑐𝑐𝑙𝑙 �𝑁𝑁𝑙𝑙 ℒ 𝑙𝑙=1 �𝑎𝑎𝑛𝑛,𝑠𝑠,𝑙𝑙𝑏𝑏𝑛𝑛,𝑢𝑢,𝑙𝑙 𝑒𝑒𝑗𝑗�2𝜋𝜋𝑓𝑓𝑛𝑛,𝑙𝑙𝑡𝑡+𝜃𝜃𝑛𝑛,𝑙𝑙� ì𝑁𝑁𝑙𝑙 𝑛𝑛=1 𝛿𝛿(𝜏𝜏 − 𝜏𝜏𝑙𝑙), where: 𝑎𝑎𝑛𝑛,𝑠𝑠,𝑙𝑙 = 𝑒𝑒𝑗𝑗𝜋𝜋(𝑺𝑺−2𝑠𝑠+1)𝑑𝑑𝑠𝑠𝜆𝜆 �cos(𝛼𝛼𝐵𝐵𝐵𝐵)+𝜙𝜙𝑚𝑚𝑚𝑚𝑚𝑚𝐵𝐵𝐵𝐵 sin(𝛼𝛼𝐵𝐵𝐵𝐵) sin�𝜙𝜙𝑛𝑛,𝑙𝑙𝑀𝑀𝐵𝐵��, 𝑏𝑏𝑛𝑛,𝑢𝑢,𝑙𝑙 = 𝑒𝑒𝑗𝑗𝜋𝜋(𝑼𝑼−2𝑢𝑢+1)𝑑𝑑𝑢𝑢𝜆𝜆 cos�𝜙𝜙𝑛𝑛,𝑙𝑙𝑀𝑀𝐵𝐵−𝛼𝛼𝑀𝑀𝐵𝐵�, 𝑓𝑓𝑛𝑛,𝑙𝑙 = 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 cos�𝜙𝜙𝑛𝑛,𝑙𝑙𝑀𝑀𝑀𝑀 − 𝛼𝛼𝜈𝜈�. (1) Authors in [4] divide the scatter ring to ℒ pairs of segments 𝐼𝐼𝑙𝑙(𝑙𝑙 = 1 .ℒ), each pair is considered as a cluster of scatters. The 𝑙𝑙𝑡𝑡ℎ pair (𝑙𝑙 = 1 .ℒ) consists of 𝑁𝑁𝑙𝑙 scatters, 𝑐𝑐𝑙𝑙 is the attenuation factor of the 𝑙𝑙𝑡𝑡ℎ path. The channel transfer function 𝐻𝐻𝑢𝑢,𝑠𝑠𝑂𝑂𝑂𝑂(𝑓𝑓, 𝑡𝑡) is a Fourier transform of ℎ𝑢𝑢,𝑠𝑠𝑂𝑂𝑂𝑂(𝜏𝜏, 𝑡𝑡) as follows: 𝐻𝐻𝑢𝑢,𝑠𝑠𝑂𝑂𝑂𝑂(𝑓𝑓, 𝑡𝑡)= � 𝑐𝑐𝑙𝑙 �𝑁𝑁𝑙𝑙 ℒ 𝑙𝑙=1 �𝑎𝑎𝑛𝑛,𝑠𝑠,𝑙𝑙𝑏𝑏𝑛𝑛,𝑢𝑢,𝑙𝑙𝑁𝑁𝑙𝑙 𝑛𝑛=1 ì 𝑒𝑒𝑗𝑗�2𝜋𝜋(𝑓𝑓𝑛𝑛,𝑙𝑙𝑡𝑡−𝜏𝜏𝑙𝑙𝑓𝑓)+𝜃𝜃𝑛𝑛,𝑙𝑙)�. (2) 𝜙𝜙𝑛𝑛 𝑀𝑀𝑀𝑀 and 𝜙𝜙𝑛𝑛𝐵𝐵𝑀𝑀 are the arrival and departure angles of the reflection path n, which come from the scatter Sn. 𝜙𝜙𝑚𝑚𝑚𝑚𝑚𝑚𝐵𝐵𝑀𝑀 is the maximal departure angle of the transmitting signal. αv is the angle from the horizontal of the velocity vector of MS. 2.2. The SCM channel modelling approach in NLOS environment Fig. 2. SCM with one cluster of scatters [3] The SCM is depicted in Fig.2, there are 𝑆𝑆 element linear BS array and 𝑈𝑈 element linear MS array, the channel impulse respond function is given for the wideband frequency channel as, where τ is the time delay of the channel: Journal of Science & Technology 139 (2019) 031-036 33 ℎ𝑢𝑢,𝑠𝑠,𝑛𝑛𝑀𝑀𝑆𝑆𝑀𝑀 (𝑡𝑡) = �𝑃𝑃𝑛𝑛𝜎𝜎𝑀𝑀𝑆𝑆𝑀𝑀 � ⎩ ⎪ ⎨ ⎪ ⎧�𝐺𝐺𝐵𝐵𝑀𝑀(𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴) 𝑒𝑒𝑒𝑒𝑒𝑒�𝑗𝑗�𝑘𝑘𝑑𝑑𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴� + 𝛷𝛷𝑛𝑛,𝑚𝑚��ì �𝐺𝐺𝑀𝑀𝑀𝑀�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴� 𝑒𝑒𝑒𝑒𝑒𝑒�𝑗𝑗𝑘𝑘𝑑𝑑𝑢𝑢 𝑠𝑠𝑠𝑠𝑠𝑠�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴��ì 𝑒𝑒𝑒𝑒𝑒𝑒�𝑗𝑗𝑘𝑘‖𝑣𝑣‖ 𝑐𝑐𝑐𝑐𝑠𝑠�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴 − 𝜃𝜃𝑣𝑣� 𝑡𝑡� ⎭⎪⎬ ⎪ ⎫𝑀𝑀 𝑚𝑚=1 . (3) ℎ𝑢𝑢,𝑠𝑠,𝑛𝑛𝑀𝑀𝑆𝑆𝑀𝑀 (𝜏𝜏, 𝑡𝑡) = ℎ𝑢𝑢,𝑠𝑠,𝑛𝑛𝑀𝑀𝑆𝑆𝑀𝑀 (𝑡𝑡)𝛿𝛿(𝜏𝜏 − 𝜏𝜏𝑛𝑛) We assumed the lognormal shadow fading and antenna gain of both BS and MS are equal to one. The transfer function 𝐻𝐻𝑢𝑢𝑠𝑠𝑛𝑛𝑁𝑁𝑁𝑁𝑂𝑂𝑀𝑀 is given as [4]: 𝐻𝐻𝑢𝑢𝑠𝑠𝑛𝑛 𝑁𝑁𝑁𝑁𝑂𝑂𝑀𝑀(𝑓𝑓, 𝑡𝑡) = �ℎ𝑢𝑢,𝑠𝑠,𝑛𝑛(𝑡𝑡)𝑁𝑁 𝑛𝑛=1 ì exp(−j2𝜋𝜋𝜏𝜏𝑛𝑛𝑓𝑓), (4) Therefore, we have: 𝐻𝐻𝑢𝑢𝑠𝑠𝑛𝑛 𝑁𝑁𝑁𝑁𝑂𝑂𝑀𝑀(𝑓𝑓, 𝑡𝑡) = ∑ � 𝑃𝑃𝑛𝑛 𝑀𝑀 𝑁𝑁 𝑛𝑛=1 ∑ � 𝑒𝑒𝑒𝑒𝑒𝑒�𝑗𝑗[𝑘𝑘𝑑𝑑𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴� + 𝛷𝛷𝑛𝑛,𝑚𝑚]� ìexp�𝑗𝑗𝑘𝑘𝑑𝑑𝑢𝑢 sin�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴�� ìexp�𝑗𝑗𝑘𝑘‖𝑣𝑣‖ cos�𝜃𝜃𝑛𝑛,𝑚𝑚,𝐴𝐴𝐴𝐴𝐴𝐴 − 𝜃𝜃𝑣𝑣�𝜏𝜏� � ì𝑀𝑀𝑚𝑚=1exp(−j2𝜋𝜋𝜏𝜏𝑛𝑛𝑓𝑓). (5) whereby, θn,m,AoD and θn,m,AoA are the AoD and the AoA for the mth sub‐path of the nth path; Φn,m is the phase of the mth sub‐path of the nth path. The SCM method has N paths (N = 6), each path has M sub‐path (M = 20). 3. Cancellation methods for 2ì2 MIMO-OFDM system In this section, the three popular interpolation methods: Linear, Sinc and Wiener interpolation are applied to study the performance of MIMO-OFDM system. 3.1. The Linear Interpolation (LI) With the assumption of that the interpolation approach is in shift invariant, LI [6]-[9] relies on two consecutive pilot positions in both time and frequency domains. If the frequency interval of the neighboring pilot subcarrier is 𝐿𝐿 , the index of the non-pilot subcarrier between two adjacent pilots is 𝑙𝑙, the index of pilot subcarriers is 𝑒𝑒. The transfer function for non-pilot subcarriers between 𝑘𝑘𝑡𝑡ℎ and (𝑘𝑘 + 1)𝑡𝑡ℎ pilots is described as: 𝐻𝐻�(𝑘𝑘𝐿𝐿 + 𝑙𝑙) = �1 − 𝑙𝑙 𝐿𝐿 �𝐻𝐻�𝑝𝑝(𝑘𝑘) + �𝑙𝑙𝐿𝐿�𝐻𝐻�𝑝𝑝(𝑘𝑘 + 1). (6) where 𝐻𝐻𝑝𝑝(𝑘𝑘) is the transfer function of the pilot. 3.2. The Sinc Interpolation (SI) This method has been introduced in [10]-[11]. With the assumption that ℎ(𝑠𝑠);𝑠𝑠 = 1, 2 𝑁𝑁 is the channel coefficient in the all of OFDM symbols and ℎ(𝑘𝑘); 𝑘𝑘 = 1, 2 𝑁𝑁𝑝𝑝𝑝𝑝𝑙𝑙𝐴𝐴𝑡𝑡 is the channel coefficient in the pilot symbols in the time domain, the closed form expression data symbols bases on pilot positions is as following as in equation (7). The effectiveness of the channel estimation in interpolation methods depends on the 𝐿𝐿 step value as the same as the LI. ℎ(𝑠𝑠) = � � ℎ(𝑘𝑘) ì𝑁𝑁𝑝𝑝𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝 𝑘𝑘=1 𝑁𝑁 𝑛𝑛=1 sin (𝜋𝜋(𝑠𝑠 − 𝑘𝑘𝐿𝐿)𝐿𝐿 ) 𝜋𝜋(𝑠𝑠 − 𝑘𝑘𝐿𝐿) 𝐿𝐿 . (7) 3.3. The Wiener Interpolation (WI) This method has been introduced in [12]. With the assumption that 𝐻𝐻�𝑝𝑝,𝑙𝑙 is the channel coefficient at 𝑠𝑠𝑡𝑡ℎ OFDM symbol and the 𝑙𝑙 𝑡𝑡ℎ sub-carrier, 𝐻𝐻�𝑝𝑝′,𝑝𝑝 is the channel coefficient at the 𝑒𝑒𝑡𝑡ℎ sub-carrier and the 𝑠𝑠′𝑡𝑡ℎ OFDM symbol that contains the pilot data, the input of Wiener filter is described as: 𝐻𝐻�𝑝𝑝,𝑙𝑙 = ∑ 𝑤𝑤𝑝𝑝′,𝑝𝑝,𝑝𝑝,𝑙𝑙𝑝𝑝′,𝑝𝑝 𝐻𝐻�𝑝𝑝′,𝑝𝑝 , (8) Set the matrix coefficient of the filter as: 𝑊𝑊𝑝𝑝,𝑙𝑙𝑇𝑇= (𝑤𝑤1,1,𝑝𝑝,𝑙𝑙 , ,𝑤𝑤𝑝𝑝′,𝑝𝑝,𝑝𝑝,𝑙𝑙 , ,𝑤𝑤(ℓ𝑝𝑝−1)𝐴𝐴𝑝𝑝+1,�ℓ𝑓𝑓−1�𝐴𝐴𝑓𝑓+1,𝑝𝑝,𝑙𝑙) (9) , Therefore, we have : 𝐻𝐻�𝑝𝑝,𝑙𝑙 = 𝑊𝑊𝑝𝑝,𝑙𝑙𝑇𝑇 𝐻𝐻�𝑝𝑝′,𝑝𝑝 . (10) where ℓ𝑡𝑡, ℓ𝑓𝑓 are the number of OFDM symbols that contain pilots in the time and frequency axis, respectively, 𝑤𝑤𝑝𝑝′ ,𝑝𝑝,𝑝𝑝,𝑙𝑙 is the filter coefficients. 𝐷𝐷𝑓𝑓 and 𝐷𝐷𝑡𝑡 are distance of pilots in frequency and time domain, respectively. 4. Description the 𝟐𝟐 ì 𝟐𝟐 MIMO-OFDM system We consider a 2ì2 MIMO system as in Fig.3 with the transmitter and receiver. In the transmitter, signal is modulated by QAM-64, then using SFBC to advantage diversity in space and frequency domain. Journal of Science & Technology 139 (2019) 031-036 34 Mapper QAM SFBC Encoder OFDM Modulator Antenna Mapping Demapper QAM SFBC Decoder Antenna Demapping Channel Estimation OFDM Demodulator Fig. 3. The 2 ì 2 MIMO-OFDM system The receiver basically do the visa versa of the transmitter but channel estimator is added to increase the system performance by using different interpolation methods. The arrangement of user data, reference signal and zero data in frequency domain obey the rules that on the same 𝑠𝑠𝑡𝑡ℎ symbol and the same the 𝑘𝑘𝑡𝑡ℎ sub-carrier, the existing reference signal (pilot) in this antenna can be gotten by setting the other to zero and vice versa. We denote the square matrix 𝐹𝐹𝑁𝑁 with 𝑁𝑁𝑆𝑆𝑆𝑆𝑇𝑇 ì 𝑁𝑁𝑆𝑆𝑆𝑆𝑇𝑇 matrix and the RS can be generated in antenna 1 and 2, respectively as below with 𝑁𝑁𝑆𝑆𝑆𝑆𝑇𝑇 is number of symbol fast fourier transfer: 𝑋𝑋𝑝𝑝,1(𝑘𝑘) = 𝑒𝑒−𝑗𝑗𝐴𝐴𝑓𝑓𝜋𝜋𝑘𝑘2/𝑁𝑁𝐹𝐹𝐹𝐹𝐹𝐹 𝑋𝑋𝑝𝑝,2(𝑘𝑘) = 𝑒𝑒−𝑗𝑗𝐴𝐴𝑓𝑓𝜋𝜋(𝑘𝑘+𝑀𝑀)2/𝑁𝑁𝐹𝐹𝐹𝐹𝐹𝐹 𝑀𝑀 = 𝑁𝑁𝑆𝑆𝑆𝑆𝑇𝑇/𝐷𝐷𝑓𝑓 (11) The channel coefficients at the pilot possitions is as: 𝐻𝐻𝑝𝑝(𝑘𝑘) = (𝑄𝑄𝐻𝐻𝑄𝑄)−1𝑄𝑄𝐻𝐻𝑌𝑌𝑟𝑟 (12) 𝑄𝑄 = �𝑑𝑑𝑠𝑠𝑎𝑎𝑑𝑑 �𝑋𝑋𝑝𝑝,1(𝑘𝑘)� ì 𝐹𝐹𝑁𝑁 ,𝑑𝑑𝑠𝑠𝑎𝑎𝑑𝑑 �𝑋𝑋𝑝𝑝,2(𝑘𝑘)� ì 𝐹𝐹𝑁𝑁 � Table 1. Simualtion parameters for channel modelling methods Parameters Value Bandwidth 5 MHz Maximum access delay 𝜏𝜏max = 2473.96 ns Antenna array distance BS 𝛥𝛥𝑑𝑑𝑠𝑠 = 10λ Antenna array distance MS 𝛥𝛥𝑑𝑑𝑢𝑢 = 0.5λ No of OFDM symbols 11 Number of sub-carrier 300 Length of guard interval (GI) 128 Number of IFFT 512 Frequency sampling 𝑇𝑇𝑠𝑠 = 130.21 𝑠𝑠𝑠𝑠 5. Simulation results and discussions Under the simulated condition of the Vehicle A model C with the speed of 30𝑘𝑘𝑘𝑘/ℎ at 2𝐺𝐺𝐻𝐻𝐺𝐺, the channel is independent in time domain and the channel profile delay is described by LTE-A. The parameters for simulation for channel modelling and the MIMO- OFMD system can be given as in Table 1 with number IFFT is number of symbol inverse fast Fourier transfer. Fig.4 - Fig.9 are the results of the comparing the two channel modelling methods when using Linear, SI and Wiener interpolations, respectively in time domain with the window step 𝐿𝐿 from 2 to 4. In Fig.4 and Fig.5 the effectiveness of the Linear cancelation methods of the MIMO 2x2 is compared in the Onering and the SCM. The Onering has the SERs higher than the SCM with the same window step of LI are from 𝐿𝐿 = 2 to 𝐿𝐿 = 4, respectively. With the increasing of step window L, the higher of the SERs, because of the more decrease of the exactitude results. Fig.6 and Fig.7 are the SERs comparison of SI in two channel modellings. As one can see the SERs of SCM is lower than of the Onering. One can see the smaller of L, the better of the performance’s system. Fig.8 and Fig.9 are the SERs comparison of Wiener interpolation which have the same conclusions as the LI and SI. The SCM has better performance than the Onering with each L and the SERs are lower at the L=2. Also,we can get the results of each window step 𝐿𝐿, the SERs of the LI are higher than the SI, the SERs of the WI are lowest of the three interpolation methods. We can see that if the step 𝐿𝐿 is increased the system performance is decreased. In Onering channel model, the SER results are higher than those obtained in the SCM as can be seen in Table 2 in the case of 𝑆𝑆𝑁𝑁𝑅𝑅 =14 𝑑𝑑𝑑𝑑. Fig. 4. SER of LI of ORM 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SE R Linear Interpolation Onering channel model LTE-A Linear Interpolation L = 2 Linear Interpolation L = 3 Linear Interpolation L = 4 Journal of Science & Technology 139 (2019) 031-036 35 Fig. 5. SER of LI of SCM Fig. 6. SER of SI of ORM Table 2. SERs of interpolation methods, 𝑆𝑆𝑁𝑁𝑅𝑅 = 14 dB when window step 𝐿𝐿 = 2 to 𝐿𝐿 = 4 SERs LI SI WI L 2 3 4 2 3 4 2 3 4 ORM .28 .7 .89 .24 .41 .69 .18 .19 .22 SCM .22 .3 .56 .17 .19 .25 .17 .18 .21 Fig. 7. SER of SI of SCM Fig. 8. SER of WI of ORM Fig. 9. SER of WI of SCM 6. Conclusions Our paper studies interpolation methods applied to estimate the channel coefficients of MIMO 2x2 systems in both channel modelling methods: the SCM and the Onering channel model in the suburban macro- cell. From the SER results, of the three interpolation methods, the WI has the best result, the following is the SI in the same above characteristic of the channel. The SER results depend on the pilot positions by the step 𝐿𝐿 in the rule of the higher of the 𝐿𝐿 step, the worse of the performance system can get. As mention above, in the case of NLOS, the system performance of MIMO channel is researched in two channel modelling, the effectiveness of the cancellation methods in the SCM is better than in the Onering channel model. References [1] Pọtzold M, Mobile Radio Channels, 2nd edn, Wiley, 2012. 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SE R Linear Interpolation SCM channel model LTE-A Linear Interpolation L = 2 Linear Interpolation L = 3 Linear Interpolation L = 4 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SE R Sinc Interpolation Onering channel model LTE-A Sinc Interpolation L = 2 SInc Interpolation L = 3 Sinc Interpolation L = 4 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SE R Sinc Interpolation SCM channel model LTE-A Sinc Interpolation L = 2 Sinc Interpolation L = 3 Sinc Interpolation L = 4 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 SE R Wiener Interpolation in Onering LTE-A Channel coefficient L = 2 Channel coefficient L = 3 Channel coefficient L = 4 0 2 4 6 8 10 12 14 SNR in dB 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SE R Wiener Interpolation SCM channel model LTE-A Wiener Interpolation L = 2 Wiener Interpolation L = 3 Wiener Interpolation L = 4 Journal of Science & Technology 139 (2019) 031-036 36 [2] Thuong N., Van Duc N., Phuong Dang, Luong PhamVan, Thu Nga N., & Patzold, M. (2012), A performance study of LTE MIMO-OFDM systems using the extended one-ring MIMO channel model. In The 2012 International Conference on Advanced Technologies for Communications (ATC 012) (pp. 263–268). [3] 3GPP, Technical Specification Group Radio Access Network Spatial channel model for Multiple Input Multiple Output (MIMO) simulation, pp. 25-996, Release 10, Mar. 2011. [4] Nguyen, T. Nga., & Nguyen, V. D. (2016), Research article, A performance comparison of the SCM and the Onering channel modeling method for MIMO- OFDMA systems, (October), 3123–3138. [5] Jiang Y, Varanasi MK, Li J, Performance Analysis of ZF and MMSE Equalizers for MIMO System: An In- Depth Study of the High SNR Regime, IEEE Transactions on Information Theory 2011, 2008–2026. [6] Alan V. Oppenheim and Ronald W. Schafer, Discreate Time signal processing, chapter 7, pp. 473-475, Prentice Hall, 1999. [7] S. Hayking, Adaptive Filter Theory, Prentice Hall, 1986, USA. [8] Hajizadeh, F. R., Mohamedpor, S. K., & Tarihi, T. M. R. (2010), Channel Estimation in OFDM System Based on the Linear Interpolation, FFT and Decision Feedback, 484–488, 18th Telecommunications forum TELFOR 2010. [9] Zhang, X., & Yuan, Z. (n.d.), The Application of Interpolation Algorithms in OFDM Channel Estimation, ijssst, Vol-17, No-38, paper11, pp. 1–5. [10] Nasreddine, M., Bechir, N., Hakimiand, W., & Ammar, M. (2014), Channel Estimation for Downlink LTE System Based on LAGRANGE Polynomial Interpolation, ICWMC 2014: The Tenth International Conference on Wireless and Mobile Communications, 65–69. [11] Schanze, T. (1995), Sinc interpolation of discrete periodic signals, IEEE Transactions on Signal Processing, 43(6), 1502–1503. [12] Li du and Louis Scharf, (1990), Wiener Filters for Interpolation and Extrapolation, Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers.